The incident had taken place on November 11.
The 13-year-old accused has been arrested and produced in a juvenile court, which has sent him to a correctional home. He has been booked under Protection of Children from Sexual Offences Act (POCSO) Act, police said.
"The boy lured the victim living next door with biscuits and took her to a farm in the afternoon on November 11 and raped her there," sub inspector Sabita Kubar, who is investigating the case, said.
The victim's mother then approached the police and registered a complaint on yesterday evening, Kubar added.
The victim has been admitted to a hospital for treatment.